We also consider the NOAA sea surface temperature data set for field reconstruction from limited sensor measurements.
The spatial resolution of data set is \(360\times 180\)  based on a one degree grid and is obtained from satellite and ship observations.
Training data set is prepared from 20 years of data (1040 snapshots spanning 1981 to 2001), while the test data set is obtained from 874 snapshots from years 2001 to 2018.
The problem setting here is inspired by Callaham et al. [1]} who capitalized on sparse representations to reconstruct fluid flow fields from local sensors.
For the task with the sea surface temperature, the PNN predicts the temporal evolution of 4 POD coefficients \({\mathbf {a}}^{\iota }=[a^{\iota }_1,a^{\iota }_2, a^{\iota }_{3},a^{\iota }_{4}]\)  over 100 weeks \({\mathbf {a}}_t=[{\mathbf {a}}^1,{\mathbf {a}}^2,...,{\mathbf {a}}^{100}]\)  from the local 30 sensor measurements on the first week snapshot \({\mathbf {s}}^1\) .
Following Callaham et al. [1]}, the input sensors are chosen randomly from the region between \(50{^\circ }\)  S and \(50{^\circ }\)  N.
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